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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Rationality of MUMs and 2-functions - Johannes Wal
cher (Universität Heidelberg)
DTSTART;TZID=Europe/London:20220721T090000
DTEND;TZID=Europe/London:20220721T100000
UID:TALK175652AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/175652
DESCRIPTION:Points of maximal unipotent monodromy in Calabi-Ya
u moduli space play a central role in mirror symme
try\, and also harbor some interesting arithmetic.
In the classic examples\, suitable expansion coef
ficients of the (all-genus) prepotential (in polyl
ogarithms) under the mirror map are integers with
an enumerative interpretation on the mirror manifo
ld. This correspondence should be expected to exte
nd to periods relative to algebraic cycles capturi
ng the enumerative geometry relative to Lagrangian
submanifolds. This expectation is challenged\, ho
wever\, when the mixed degeneration is not defined
over Q. After musing about compatibility with mir
ror symmetry\, I will discuss two recent results t
hat sharpen these questions further: The first is
a theorem proven by Felipe Mü\;ller which stat
es that the coefficients of rational 2-functions a
re necessarily contained in an abelian number fiel
d. (As defined in the talk\, 2-functions are forma
l power series whose coefficients satisfy a natura
l Hodge theoretic supercongruence.) The second are
examples worked out in collaboration with Bö\
;nisch\, Klemm\, and van Straten\, of MUMs that ar
e themselves not defined over Q.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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